Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 10 - Section 10.5 - Rationalizing Numerators and Denominators of Radical Expressions - Exercise Set: 68

Answer

$\dfrac{\sqrt{5}+2}{\sqrt{2}}=\dfrac{1}{\sqrt{10}-2\sqrt{2}}$

Work Step by Step

$\dfrac{\sqrt{5}+2}{\sqrt{2}}$ Multiply the numerator and the denominator by the conjugate of the numerator and simplify if possible: $\dfrac{\sqrt{5}+2}{\sqrt{2}}=\dfrac{\sqrt{5}+2}{\sqrt{2}}\cdot\dfrac{\sqrt{5}-2}{\sqrt{5}-2}=\dfrac{(\sqrt{5})^{2}-2^{2}}{\sqrt{2}(\sqrt{5}-2)}=...$ $...=\dfrac{5-4}{\sqrt{10}-2\sqrt{2}}=\dfrac{1}{\sqrt{10}-2\sqrt{2}}$
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